arXiv research

We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DP…

New method for computing terminal embeddings in sublinear time.

This work addresses dynamic KDE data structures with robustness to adversarial queries.

New algorithms solve linear algebra problems in sublinear time.

Quantum algorithm speeds up Gibbs partition function estimation.

InstantEmbedding efficiently generates node representations with less computation and memory.

Paper presents a faster classical algorithm for principal component regression.

New algorithms reduce rejection sampling complexity for shape-constrained distributions.

We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also extends to Circulant, Toeplitz and Hankel matrices, and the broader family of s…

Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time i…

Quantum algorithms reduce clustering input size, achieving near-linear approximation.

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

This work tackles scalable sampling for nonsymmetric DPPs.

We study the $\ell_0$-Low Rank Approximation Problem, where the goal is, given an $m \times n$ matrix $A$, to output a rank-$k$ matrix $A'$ for which $\|A'-A\|_0$ is minimized. Here, for a matrix $B$, $\|B\|_0$ denotes the number of its non-zero entries. This NP-hard variant of low rank approximation is natural for pro…

Paper presents a new training method for overparametrized neural networks that reduces time per iteration.

Sublinear algorithms detect cliques in graphs with high probability.

New data structure identifies close match from multiple distributions.

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fr…

Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as tree-based solutions have been investigated in the recent literature, to perform ap…

Locality sensitive hashing (LSH) is a powerful tool for sublinear-time approximate nearest neighbor search, and a variety of hashing schemes have been proposed for different dissimilarity measures. However, hash codes significantly depend on the dissimilarity, which prohibits users from adjusting the dissimilarity at q…

We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization problems are equivalent, in the following sense. Given any instance of an $\ell…

Latent Dirichlet Allocation (LDA) is a popular tool for analyzing discrete count data such as text and images. Applications require LDA to handle both large datasets and a large number of topics. Though distributed CPU systems have been used, GPU-based systems have emerged as a promising alternative because of the high…

Improved private geometric median estimation with nearly-linear time complexity.

We study the complexity of sampling from a distribution over all index subsets of the set $\{1,...,n\}$ with the probability of a subset $S$ proportional to the determinant of the submatrix $\mathbf{L}_S$ of some $n\times n$ p.s.d. matrix $\mathbf{L}$, where $\mathbf{L}_S$ corresponds to the entries of $\mathbf{L}$ ind…

The method of random projections has become a standard tool for machine learning, data mining, and search with massive data at Web scale. The effective use of random projections requires efficient coding schemes for quantizing (real-valued) projected data into integers. In this paper, we focus on a simple 2-bit coding …

The $k$-Nearest Neighbor Search ($k$-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed t…

Recently, the method of b-bit minwise hashing has been applied to large-scale linear learning and sublinear time near-neighbor search. The major drawback of minwise hashing is the expensive preprocessing cost, as the method requires applying (e.g.,) k=200 to 500 permutations on the data. The testing time can also be ex…

New algorithms sample spike-and-slab priors efficiently in high dimensions.

New method robust to semi-random sparse recovery, nearly-linear time.

The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.

Active sampling algorithm for linear regression with various norms and improved query complexity.